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Re: If J#0, what is the value of J ? [#permalink]
23 Jul 2012, 16:16

1

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Expert's post

0^0 is equal to 1 in most mathematical conventions, but not all. Therefore, you can expect that GMAT not to test the subject--it won't show up, and you won't be expected to know it!
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QUESTION YOU ARE TALKING ABOUT SHOULD READ: If J\neq{0}, what is the value of J ?

(1) |J| = J^{-1} (2) J^J = 1

Two reasons why should the stem state that J\neq{0}: For statement (1) if J=0 then we'll have 0^{-1}=\frac{1}{0}=undefined. Remember you can't raise zero to a negative power. For statement (2) if J=0 then we'll have 0^0. 0^0, in some sources equals to 1, some mathematicians say it's undefined. Anyway you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT. So on the GMAT the possibility of 0^0 is always ruled out.

Also notice that saying in the stem that J is an integer is a redundant.

AS FOR THE SOLUTION: If J\neq{0}, what is the value of J ?

(1) |J| = J^{-1} --> |J|*J=1 --> J=1 (here J can no way be a negative number, since in this case we would have |J|*J=positive*negative=negative\neq{1}). Sufficient.

(2) J^J = 1 --> again only one solution: J=1. Sufficient.